A Statistical Examination on the Compensation between the Enthalpies and Entropies Obtained from the Calorimetric Methods

The widely observed enthalpy-entropy compensation in chemistry and biophysics is still in a state of great confusion, because the reported enthalpy-entropy correlations in literature were often found to be false1-3. This problem has promoted Exner4. Krug5, Linert6, and others to develop some statistical methods to examine the compensation between the enthalpies and entropies obtained from the indirect van't Hoff method. However, as pointed out by Connors in a recent review7, it remains untou…     

Enthalpy–Entropy Compensation Combined with Cohesive Free‐Energy Densities for Tuning the Melting Temperatures of Cyanobiphenyl Derivatives

This work illustrates how minor structural perturbations produced by methylation of 4′‐(dodecyloxy)‐4‐cyanobiphenyl leads to enthalpy–entropy compensation for their melting processes, a trend which can be analyzed within the frame of a simple intermolecular cohesive model. The transformation of the melting thermodynamic parameters collected at variable temperatures into cohesive free‐energy densities expressed at a common reference temperature results in a novel linear correlation, from which melting temperatures can be simply predicted from molecular volumes.     

枯草杆菌α-淀粉酶在一些色谱体系中的热力学和超热力学研究

通过测定不同温度范围的热力学平衡常数、焓变、熵变、自由能变和补偿温度,研究了枯草杆菌α-淀粉酶在几种色谱介质上的热力学和超热力学。结果表明,在RP-C18反相介质、Zn2+螯合的Sepharose fast-flow亲和介质和WCX-1阳离子交换介质上,当温度分别在13-30和30-50℃范围时,它们的lnKSL分别随绝对温度的倒数线性变化;而在PEG-400和修饰的PEG-400疏水色谱介质上,当温度分别在13-40和13-30℃范围时,它们的lnKSL分别随绝对温度的倒数线性减小,但当温度分别高于40℃和30℃时,它们则随绝对温度的倒数剧烈减小。通过研究不同温度范围的焓变、熵变、自由能变和α-淀粉酶构象变化之间的关系,发现在RP-C18反相和Zn2+螯合的Sepharose fast-flow亲和介质上在30- 50 ℃温度范围内,在WCX-1阳离子交换介质上在13-30 ℃温度范围内,α-淀粉酶的吸附过程由焓变和熵变共同所支配,而在Zn2+螯合的Sepharose fast-flow亲和介质上在13- 30 ℃温度范围内,在WCX-1阳离子交换介质上在30-50 ℃温度范围和在PEG-400 和修饰的PEG-400疏水色谱介质上在13-65 ℃温度范围时,α-淀粉酶的吸附过程仅仅由熵变所控制。最后,通过α-淀粉酶在这些色谱体系中的补偿温度进一步发现,它们的焓变仅仅只能通过它们构象变化所引起的熵变所补偿。     

The paradoxical thermodynamic basis for the interaction of ethylene glycol, glycine, and sarcosine chains with bovine carbonic anhydrase II: an unexpected manifestation of enthalpy/entropy compensation

This paper describes a systematic study of the thermodynamics of association of bovine carbonic anhydrase II (BCA) and para-substituted benzenesulfonamides with chains of oligoglycine, oligosarcosine, and oligoethylene glycol of lengths of one to five residues. For all three of these series of ligands, the enthalpy of binding became less favorable, and the entropy less unfavorable, as the chain length of the ligands increased. The dependence on chain length of the enthalpy was almost perfectly compensated by that of the entropy; this compensation resulted in dissociation constants that were independent of chain length for the three series of ligands. Changes in heat capacity were independent of chain length for the three series and revealed that the amount of molecular surface area buried upon protein-ligand complexation did not increase with increasing chain length. Taken together, these data refute a model in which the chains of the ligands interact hydrophobically with the surface of BCA. To explain the data, a model is proposed based on decreasing "tightness" of the protein-ligand interface as the chain length of the ligand increases. This decreasing tightness, as the chain length increases, is reflected in a less favorable enthalpy (due to fewer van der Waals contacts) and a less unfavorable entropy (due to greater mobility of the chain) of binding for ligands with long chains than for those with short chains. Thus, this study demonstrates a surprising example of enthalpy/entropy compensation in a well-defined system. Understanding this compensation is integral to the rational design of high-affinity ligands for proteins.     

The natural DNA bending angle in the lac repressor headpiece-O1 operator complex is determined by protein-DNA contacts and water release

We performed molecular dynamics simulations of the lac repressor headpiece-O1 operator complex for natural, over and underbent DNA to assess the factors that determine the natural DNA bending angle. At the natural angle, the specific and nonspecific contacts between the protein and DNA are optimized. Protein-DNA contacts show different angle dependences in the right and left sites, with the left site generally getting weaker and the right site getting stronger as the bending angle increases. Two entropic factors were identified as well: at the natural bending angle, water release and the quasiharmonic protein configurational entropy are maximized. The gain in protein configurational entropy might stem from an entropy-entropy compensation mechanism, in which a reduction in protein fluctuations is offset by a loss in correlations between the right and left sites.     

Enthalpy–entropy compensation for n-hexane adsorption on HZSM-5 containing transition metal ions

In this work, the values of entropy changes related to n-hexane adsorption onto ion-exchanged ZSM-5 zeolites were calculated from differential heats, obtained from microcalorimetric experiments. The existence of enthalpy–entropy compensation effect, evidenced by the linearity of −ΔH vs. −ΔS plots and characteristic for all investigated ZSM-5 zeolites, was found. In the case of ZSM-5 structure, modifying the zeolite structure by ion-exchange gives rise to changes in the heats of adsorption and adsorption entropy in the same manner. The factors that can influence the appearance of entropy–enthalpy compensation were discussed. It was found that compensation effect is governed by ion-induced dipole interaction between highly polarising cationic centres in zeolite and nonopolar n-hexane molecules, and hence, depends on the size, charge and electron configuration of the cation. It was found also that the compensation temperature is in correlation with the number of zeolites’ strong acid centres. Contrary to the adsorption of n-hexane on ZSM-5 zeolites, compensation effect was not found for the adsorption of the same gas on faujasite-type zeolites.     

Simple Accurate Verification of Enthalpy-Entropy Compensation and Isoequilibrium Relationship

In many experimental investigations of thermodynamic equilibrium or kinetic properties of series of similar reactions it is found that the enthalpies and entropies derived from Van ′t Hoff or Arrhenius plots exhibit a strong linear correlation. The origin of this Enthalpy-Entropy compensation, which is strongly related to the coalescence tendency of Van ′t Hoff or Arrhenius plots, is not necessarily due to a physical/chemical/biological process. It can also be a merely statistical artefact. A new method, called Combined K-CQF makes it possible both to quantify the degree of coalescence of experimental Van ‘t Hoff lines and to verify whether or not the Enthalpy-Entropy Compensation is of a statistical origin at a desired confidence level. The method is universal and can handle data sets with any degree of coalescence of Van ‘t Hoff (or Arrhenius) plots. The new method requires only a standard least square fit of the enthalpyΔH versus entropy ΔS plot to determine the two essential dimensionless parameters K and CQF. The parameter K indicates the position (in inverse temperature) of the coalescence region of Van ‘t Hoff plots and CQF is a quantitative measure of the smallest spread of the Van ‘t Hoff plots. The position of the (K, CQF) couple with respect to universal confidence contours determined from a large number of simulations of random Van ‘t Hoff plots indicates straightforwardly whether or not the ΔH-ΔS compensation is a statistical artefact.     

Free energy, entropy, and induced fit in host-guest recognition: calculations with the second-generation mining minima algorithm

This study applies a novel computational method to study molecular recognition for three sets of synthetic hosts: molecular clips, molecular tweezers, and a synthetic barbiturate receptor. The computed standard free energies of binding for the 12 binding reactions agree closely with experiment and provide insight into the roles of configurational entropy, preorganization, and induced fit in the systems studied. The computed changes in configurational entropy are comparable in magnitude to the changes in mean potential plus solvation energy, and they result primarily from changes in the average width of the energy wells upon binding. A strong correlation is observed between the changes in configurational energy and configurational entropy upon binding, resulting in near-linear compensation analogous to classical entropy-enthalpy compensation.     

The role of protein “Stability patches” in molecular recognition: A case study of the human growth hormone‐receptor complex

Dynamic characteristics of protein surfaces are among the factors determining their functional properties, including their potential participation in protein‐protein interactions. The presence of clusters of static residues—“stability patches” (SPs)—is a characteristic of protein surfaces involved in intermolecular recognition. The mechanism, by with SPs facilitate molecular recognition, however, remains unclear. Analyzing the surface dynamic properties of the growth hormone and of its high‐affinity variant we demonstrated that reshaping of the SPs landscape may be among the factors accountable for the improved affinity of this variant to the receptor. We hypothesized that SPs facilitate molecular recognition by moderating the conformational entropy of the unbound state, diminishing enthalpy–entropy compensation upon binding, and by augmenting the favorable entropy of desolvation. SPs mapping emerges as a valuable tool for investigating the structural basis of the stability of protein complexes and for rationalizing experimental approaches, such as affinity maturation, aimed at improving it. © 2015 Wiley Periodicals, Inc.     

Electrical resistivity correlations in rigid and plasticized polymers

Empirical correlations in the literature between room-temperature electrical resistivity and activation energy in various polymers are shown to be equivalent to the compensation law. Assuming that electrical conduction is an ionic process, following the Eyring theory, the compensation law can be expressed as a direct proportionality between activation energy and activation entropy. It is found that plasticizers do not change the ion number density or the ionic jump distance but only the temperature at which energy and entropy effects balance. An approximation of the ion number density is consistent with the idea that the mobile ions result from the dissociation of absorbed water.     

Selective Formation of a Trisubstituted Alkene Motif by trans‐Hydrostannation/Stille Coupling: Application to the Total Synthesis and Late‐Stage Modification of 5,6‐Dihydrocineromycin B

Countless natural products of polyketide origin have an E‐configured 2‐methyl‐but‐2‐en‐1‐ol substructure. An unconventional entry into this important motif was developed as part of a concise total synthesis of 5,6‐dihydrocineromycin B. The choice of this particular target was inspired by a recent study, which suggested that the cineromycin family of antibiotics might have overlooked lead qualities, although our biodata do not necessarily support this view. The new approach consists of a sequence of alkyne metathesis followed by a hydroxy‐directed trans‐hydrostannation and a largely unprecedented methyl‐Stille coupling. The excellent yield and remarkable selectivity with which the signature trisubstituted alkene site of the target was procured is noteworthy considering the rather poor outcome of a classical ring‐closing metathesis reaction. Moreover, the unorthodox ruthenium‐catalyzed trans‐hydrostannation is shown to be a versatile handle for diversity‐oriented synthesis.     

Molecular Hydrogels from Bolaform Amino Acid Derivatives: A Structure–Properties Study Based on the Thermodynamics of Gel Solubilization

Insight is provided into the aggregation thermodynamics associated to hydrogel formation by molecular gelators derived from L ‐valine and L ‐isoleucine. Solubility data from NMR measurements are used to extract thermodynamic parameters for the aggregation in water. It is concluded that at room temperature and up to 55 °C, these systems form self‐assembled fibrillar networks in water with quite low or zero enthalpic component, whereas the entropy of the aggregation is favorable. These results are explained by considering that the hydrophobic effect is dominant in the self‐assembly. However, studies by NMR and IR spectroscopy reveal that intermolecular hydrogen bonding is also a key issue in the aggregation process of these molecules in water. The low enthalpy values measured for the self‐assembly process are ascribed to the result of a compensation of the favorable intermolecular hydrogen‐bond formation and the unfavorable enthalpy component of the hydrophobic effect. Additionally, it is shown that by using the hydrophobic character as a design parameter, enthalpy‐controlled hydrogel formation, as opposed to entropy‐controlled hydrogel formation, can be achieved in water if the gelator is polar enough. It is noteworthy that these two types of hydrogels, enthalpy‐versus entropy‐driven hydrogels, present quite different response to temperature changes in properties such as the minimum gelator concentration (mgc) or the rheological moduli. Finally, the presence of a polymorphic transition in a hydrogel upon heating above 70 °C is reported and ascribed to the weakening of the hydrophobic effect upon heating. The new soft polymorphic materials present dramatically different solubility and rheological properties. Altogether these results are aimed to contribute to the rational design of molecular hydrogelators, which could be used for the tailored preparation of this type of soft materials. The reported results could also provide ground for the rationale of different self‐assembly processes in aqueous media.     

Confusing cause and effect: energy-entropy compensation in the preferential solvation of a nonpolar solute in dimethyl sulfoxide/water mixtures

We performed molecular simulations to analyze the thermodynamics of methane solvation in dimethyl sulfoxide (DMSO)/water mixtures (298 K, 1 atm). Two contributions to the interaction thermodynamics are studied separately: (i) the introduction of solute-solvent interactions (primary contribution) and (ii) the solute-induced disruption of cohesive solvent-solvent interactions (secondary contribution). The energy and entropy changes of the secondary contribution always exactly cancel in the free energy (energy-entropy compensation), hence only the primary contribution is important for understanding changes of the free energy. We analyze the physical significance of the solute-solvent energy and solute-solvent entropy associated with the primary contribution and discuss how to obtain these quantities from experiments combining solvation thermodynamic and solvent equation of state data. We show that the secondary contribution dominates changes in the methane solvation entropy and enthalpy: below 30 mol % DMSO in the mixture, methane, because of more favorable dispersion interactions with DMSO molecules, preferentially attracts DMSO molecules, which, in response, release water molecules into the bulk, causing an increase in the entropy. This large energy-entropy compensating process easily causes a confusion in the cause for and the effect of preferred methane-DMSO interactions. Methane-DMSO dispersion interactions are the cause, and the entropy change is the effect. Procedures that infer thermodynamic driving forces from analyses of the solvation entropies and enthalpies should therefore be used with caution.     

Enthalpy-entropy compensation in micellization of sodium dodecyl sulphate in water/methanol,water/ethylene glycol and water/glycerol binary mixtures

The enthalpy-entropy compensation in micellization of sodium dodecyl sulphate (SDS) in binary mixtures of water/methanol (MeOH), water/ethylene glycol (EG) and water/glycerol (GL) over a temperature range of 10–60°C was examined. When the cosolvent concentration was low, the critical micelle concentration (CMC) depended only on the total amount of the hydroxyl group added. When the cosolvent concentration was high, the increase in CMC followed the sequence: MeOH>EG>GL. Enthalpy and entropy changes were evaluated from which the compensation temperature was determined. Both enthalpy and entropy changes decreased on the addition of the cosolvents, indicating a lowering of solution hydrophobicity. The compensation temperature was found as a constant over the cosolvent concentration range, as a result, was not a good index for characterizing the solute/solvent interactions. The two reference temperatures at which the enthalpy-entropy change respectively became zero were strongly influenced by the cosolvent addition, therefore could serve as a proper index for solution hydrophobicity.     

On the choice of a reference state for one‐step perturbation calculations between polar and nonpolar molecules in a polar environment

One‐step perturbation is an efficient method to estimate free energy differences in molecular dynamics (MD) simulations, but its accuracy depends critically on the choice of an appropriate, possibly unphysical, reference state that optimizes the sampling of the physical end states. In particular, the perturbation from a polar moiety to a nonpolar one and vice versa in a polar environment such as water poses a challenge which is of importance when estimating free energy differences that involve entropy changes and the hydrophobic effect. In this work, we systematically study the performance of the one‐step perturbation method in the calculation of the free enthalpy difference between a polar water solute and a nonpolar “water” solute molecule solvated in a box of 999 polar water molecules. Both these polar and nonpolar physical reference states fail to predict the free enthalpy difference as obtained by thermodynamic integration, but the result is worse using the nonpolar physical reference state, because both a properly sized cavity and a favorable orientation of the polar solute in a polar environment are rarely, if ever, sampled in a simulation of the nonpolar solute in such an environment. Use of nonphysical soft‐core reference states helps to sample properly sized cavities, and post‐MD simulation rotational and translational sampling of the solute to be perturbed leads to much improved free enthalpy estimates from one‐step perturbation. © 2012 Wiley Periodicals, Inc.     

Solvophobic Acceleration of a Diels–Alder Reaction in True Solutions in Organic Solvents

The rate of Diels–Alder reaction of diene 9,10‐bis(hydroxymethyl)anthracene with dienophile N‐ethylmaleimide was studied in a series of solvents with different polarity and hydrogen‐bonding ability. Enthalpies and entropies of activation were determined from the temperature dependences of the rate constants. Rate acceleration in nonaqueous protic solvents such as glycerol, propylene, and ethylene glycols was observed. In addition, enthalpy versus entropy of activation plots show a compensation pattern different from the other considered solvents, which can be linked with the solvophobic effects observed in polyhydric alcohols. However, the solvophobic acceleration was not as strong as the hydrophobic acceleration in water. Hydrogen bonding of the reactants and transition state with solvent also influences the reaction rate. The studied reaction is slightly promoted in hydrocarbon solvents in comparison with aprotic polar solvents. This was explained by hydrogen bonding of the hydroxyl groups of diene with dienophile in transition state, which requires prior breaking of the hydrogen bonds of these groups with polar solvent molecules.     

Structural relaxation behavior of strain hardened shape memory polymer fibers for self‐healing applications

In this study, shape‐memory polyurethane (SMPU) fibers were strain hardened by cold‐drawing programming (CDP) process. The programmed fibers are experimentally studied on the physical and thermomechanical properties. Structural relaxation, which determines shape memory capability of the SMP fibers, is quantified by conformational entropy change. Based on the entanglement tube theory and reptation theory, the entropic force is derived as a “bridge” to link the stress relaxation and structural relaxation, and thus structural relaxation can be evaluated by stress relaxation. It was found that the CDP SMPU fibers would still have good crackclosing capability after 13 years of hibernation in polymer matrix composite. © 2013 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2013 , 51, 966–977     

Interpretation of the TSDC fractional polarization experiments on the α‐relaxation of polymers

We report on the interpretation of the thermally stimulated depolarization current (TSDC) experiments, with partial polarization methods, on the dielectric α‐relaxation. The results obtained on polyvinyl acetate are rationalized on the basis of the Boltzmann superposition principle in combination with a Kohlrausch–Williams–Watts (KWW) time decay of the polarization (with the β exponent essentially temperature independent and equal to the value determined by conventional dielectric methods at T_g). From this analysis of the global TSDC spectrum we found a complex temperature dependence of the KWW relaxation time, which is Arrhenius‐like at the lowest temperatures but crosses over to the Vogel–Fulcher behavior observed above T_g in the temperature range of the TSDC peak. On the basis of these results, we found the way of predicting the TSDC spectra measured after partial polarization procedures. We found that, the distribution of activation energies and compensation behavior deduced by following the standard way of analysis are associated to the assumption of an Arrhenius‐like temperature dependence of the α‐relaxation time in the temperature range explored by TSDC. Therefore we conclude that both the distribution of activation energies and compensation behavior obtained by following the standard way of analysis do not give a proper physical picture of the α‐relaxation of glassy polymers around the glass‐transition temperature. Our results also show that the partial polarization TSDC methods are not able to give insight about the actual existence or not of a distribution of relaxation times at the origin of the nonexponentiality of the α‐relaxation of polymers. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2105–2113, 2000     

Hydrogen Bonding in Liquid Water and in the Hydration Shell of Salts

A near‐IR spectral study on pure water and aqueous salt solutions is used to investigate stoichiometric concentrations of different types of hydrogen‐bonded water species in liquid water and in water comprising the hydration shell of salts. Analysis of the thermodynamics of hydrogen‐bond formation signifies that hydrogen‐bond making and breaking processes are dominated by enthalpy with non‐negligible heat capacity effects, as revealed by the temperature dependence of standard molar enthalpies of hydrogen‐bond formation and from analysis of the linear enthalpy–entropy compensation effects. A generalized method is proposed for the simultaneous calculation of the spectrum of water in the hydration shell and hydration number of solutes. Resolved spectra of water in the hydration shell of different salts clearly differentiate hydrogen bonding of water in the hydration shell around cations and anions. A comparison of resolved liquid water spectra and resolved hydration‐shell spectra of ions highlights that the ordering of absorption frequencies of different kinds of hydrogen‐bonded water species is also preserved in the bound state with significant changes in band position, band width, and band intensity because of the polarization of water molecules in the vicinity of ions.